Is it possible to add key frames to initial shape setting?
Not as keyframes, but you can create presets when you add a shape, by pressing the + sign right next to the operator presets.



By creating a preset you can recall custom settings.

Note that once you modify an object in any way there is no way to go back and re-edit the parameters of the created object. 

Read: Is there any way to edit parameters for an object after it is created?

If you want to create an animation by modifying the shape look into using shapekeys 

https://docs.blender.org/manual/en/latest/animation/shape_keys/index.html